A modified variational iteration method for the analysis of viscoelastic beams

•An algorithm based on VIM and Laplace transformation is created for the dynamic study of viscoelastic beams.•It is avoided the definition of initial approximation in the using of VIM, which is a difficult step for nonlinear problems.•There are no errors, which usually accompany the methods based on...

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Bibliographic Details
Published in:Applied mathematical modelling Vol. 40; no. 17-18; pp. 7988 - 7995
Main Author: Martin, Olga
Format: Journal Article
Language:English
Published: Elsevier Inc 01.09.2016
Subjects:
Correspondence principle
Euler–Bernoulli beam theory
Galerkin method
Laplace transform
Variational iteration method
Viscoelastic beam
Variational iteration method
Viscoelastic beam
Galerkin method
Correspondence principle
Laplace transform
Euler–Bernoulli beam theory
ISSN:0307-904X
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Summary:•An algorithm based on VIM and Laplace transformation is created for the dynamic study of viscoelastic beams.•It is avoided the definition of initial approximation in the using of VIM, which is a difficult step for nonlinear problems.•There are no errors, which usually accompany the methods based on the discretization of time interval. Based on a constitutive law in a hereditary integral form, a mathematical model for dynamic analysis of the isotropic linear viscoelastic beams is presented. To solve the governing equation for these structures subjected to a distributed load is created an accuracy and computational efficiency algorithm that uses Galerkin's method and a modified form of the variational iteration method (VIM) for time-domain equations. Numerical results for both quasi-static and dynamic analysis are presented and these will be accompanied by the graphical representations.
ISSN:0307-904X
DOI:10.1016/j.apm.2016.04.011